# Order and Optimization (TAC: Vol. III)'' - Typos

This page lists the typographical errors that have been discovered in the Fall 2006 pre-publication version of Order and Optimization, by Douglas B. West (Volume III of The Art of Combinatorics). This page is of interest only to the few persons having a copy of this draft, such as the students in my course and possibly reviewers. Please send any additional contributions to west@math.uiuc.edu. Contributors noted in parentheses.

## Category 1: Corrections of a Mathematical Nature

• p9, Example 0.24: "a0" should be "a1" (Alexandra Seceleanu)
• p32, Exercise 11.1.5: "Ci\times Cj" should be "\underlin{i}\times \underlin{j}" (Tim LeSaulnier)
• p41, Example 11.2.20: "the k-shadow of A lies in" should be "the set A* of elements covering elements of A is precisely"
• p52, Example 11.3.4: "element of BNn" should be "member of 2n:
• p62, Theorem 11.3.18: The chain labeled D0 in the figure should be labeled D1. In the text, "a3=3" should be "a3=n-1"
• p174, Exercise 12.3.3: "2k-dimensional posets" should be "posets of dimension at most 2k".
• p188, Exercise 12.4.2b: in the hint, "at most" should be "at least" (Paul Wenger)
• p221, top: in the case of one vector having 10 and the other having 01, the intersection remains unchanged if the second vector doesn't change, so this case should also allow equality.
• p231, Theorem 13.1.31: In the middle paragraph, we must prove that B\esub T in order to put B into H. This uses the maximality of T. The final paragraph does not need the maximality of T.
• p258, Theorem 13.3.3: several instances of "I(x)" and "C(x)" should be "I(x1)" and "C(x1)"
• p259, Theorem 13.3.3: At the end of the proof, the claim that xi < I(xi-1) does not follow, but the choice of xi does imply that every element strictly below xi (such as all of I(xi+1)) is below all of I(xi-1), and this is enough
• p262, Example 13.3.9: "intervals of size n" should be "intervals of size i"
• p479, Theorem 15.3.36: in the last paragraph, C' should be Y

## Category 2: Other Changes, Comments and Corrections of Note

• p219, Theorem 13.1.8: the term "shade" was used before its definition
• p223-225, Kruskal-Katona: Uses of "reverse lexicographic" should be changed to "colex", since some readers might misinterpret "reverse lexicographic" to mean the reverse of lexicographic order" (Garth Isaak)

## Category 3: Minor Changes, Typos, and Clarifications

• p40, Theorem 11.2.17: "be real-valued weight" should be "be a real-valued weight"
• p135, Remark 12.2.9: "not surprised" should be "not surprising"
• p228, Theorem 13.1.27: "It suffice" should be "It suffices
• p259, top: "monchromatic" should be "monochromatic", and three lines later a parenthesis is missing
• p394, Definition 15.1.4: the last "that" should be deleted